As mentioned upthread, the white-majority British colonies all gained Responsible Government (an Executive Council/Cabinet appointed by and responsible to the elected Lower House) between 1848 and 1856 IOTL. The Cape Colony achieved the same in 1872, the first colony without a white majority to do so.
ITTL Florida makes history; some time between 1856 and 1872 (and I believe likely not long after 1856) Florida gains responsible government, and after Canadian Confederation, a political movement grows to provide Florida with a more robust constitutional framework. This process is completed by 1874, and during the process, Florida gains the Bahamas (including Turks & Caicos Islands).
The new constitution is unitary or quasi-federal in nature, more similar to the contemporary New Zealand constitution than the Canadian one, but different in its own way.
The former administrative districts will become 'Provinces' of Florida (the districts being the likely renamed West Florida, Middle Florida, East Florida, with South Florida split into 3, the new capitals at OTL Tampa and OTL Key West); but these will not have the same constitutional grounding as the Canadian ones; they are governed by an elected council with a Superintendent appointed by the Florida Executive. The Provinces are subdivided into counties somewhat larger than the OTL ones (at least in the North), which are subdivided further into Parishes.
The Upper House will be appointed by the Executive, as in Canada, but won't be subject geographical restrictions, at least in the first incarnation. As in Canada, members of the Upper House (called the Legislative Council in Florida) are appointed for life; this is intentionally done to mitigate the 'damage' which could be caused by further expansion of the vote, which is subject to property qualification not unlike those in Britain, Canada, or the Cape at the time.
This ensures that despite having an Afro-Floridian majority, Florida's legislature is overwhelmingly white, with the small number of mixed-race persons outnumbering Afro-Floridian MPs for several decades.
In the early era, it's entirely possible that Florida sees a late development of a true party system, and that early elections focus around a "Government" vs "Opposition" dynamic.
Over time, however, distinctive camps will form. CeeJay's Palmera, for anyone who for some reason has not yet read it but finds themselves this far into this thread, has some incredibly creative and well-constructed names for Palmera's political groupings. I have the Liberal Party and the Conservative Party. Here all day, folks.
The Liberal Party are "classical Liberals" who are broadly aligned with the contemporary Republican Party of the USA, as well as the British & Canadian Liberal parties, a party of Business which encourages links to United States. The Liberal Party, aligned with early Progressive movements, is also, as in Canada, NZ and the UK, more sympathetic to the nascent labour movement, and consequently finds a much more substantial base of support among the mixed-race population, as well as the few black and Asian Floridians who can vote.
The Conservative Party, meanwhile, has its closest connections with the British and Canadian Conservative parties. Also, of course, a pro-business party, they favour links with Canada and especially Britain. They are closely aligned with (now dis-established) Anglican Church and the 'old money' settlers of Florida.
As a result, when the deep south states begin introducing white supremacist segregationist constitutions from 1888, both major political parties in Florida, despite being controlled by white Floridians, have significant pull factors dissuading them from fulling embracing the alarming rise of 'scientific' (sic) racism.
I believe that Florida, which by this point has a long established tradition of racial equality before the law, will avoid adopting public segregation, in state institutions. The white-dominated legislatures, however, will do nothing to stop private businesses from discriminating in any way they see fit; this of course is to not offend the sensibilites of American tourists whose dollars they so eagerly seek. This will lead to an increasing proliferation of segregation, which over time will establish a societal expectation which will begin to pressure the legislature to institute formal segregation, just as political and social developments are leading to a renewed push for full equality and introduction of universal suffrage - but I'm getting ahead of myself a little.
The third, in this period largely extra-parliamentary political force, is that of the Labour movement, and its allies in the Farmers, Populist, Progressive, and Socialist movements. This Florida is significantly more industrialised at this early time than OTL Florida, and so the Labour movement is an important factor by no later than the 1890s. It is dominated from an early date by Afro-Floridians, and is closely tied to the movement for universal suffrage.